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You have it backwards.
A heavier bullet spends more time in the barrel.
.... more energy put into the bullet and less wasted.
I recommend either 77 grain Sierra matchking or 75 grain TAP
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Projectile performance is usually pretty heavily dependent on velocity. Whether it be an expanding projectile (Gold Dot, Fusion, TAP SBR, TSX, etc.) or a FMJ/BTHP/etc. projectile which relies on yaw/fragmentation to dramatically increase terminal effectiveness, they all have a minimum velocity at which they perform as desired. Typically, minimum velocities for desired performance are going to be lower with expanding projectiles than they will be with fragmenting projectiles that rely on yaw to initiate fragmentation.
It's also important to understand that heavier projectiles will be traveling at slower velocities than lighter projectiles everything else being equal (barrel length, etc.).
Knowing this, yes, when you start getting down into extremely short barrels, a lighter projectile is going to be the better choice in a lot of cases because the heavier projectiles will offer extremely limited range inside their performance envelope, with some never reaching their required velocity thresholds at all.
A heavier projectile spending more time in the bore (due to the projectile traveling at a slower velocity) has fuck all to do with how the projectile actually performs on target. I'm not even sure what you mean by "having more energy put into it."
Also, those projectiles you're recommending are never going to reach their required fragmentation thresholds out of a 7.5" barrel. The generally accepted fragmentation threshold for the 77gr SMK is somewhere around 2250fps. You're barely getting there with a 10.5" barrel and you'll never reach that velocity number with a 7.5" barrel, even at the muzzle.
ETA: OP, a high quality expanding load designed to work at lower velocities commonly found with shorter barrels is what you should be looking for (as already mentioned). Speer Gold Dot, Federal Fusion, TAP SBR, etc. are all great choices. I'm not entirely sure on the 55gr TAP Urban, but IIRC, that specific load uses a VMAX projectile which is more of a varmint bullet. You'll see impressive expansion/fragmentation, but penetration isn't exactly great.